1.what is the vertex of the graph? (see attachment)
a.(2,2)
b.(1,3)
c.(3,1)
d.(0,2)
2. is the vertex of the graph in problem 1 a maximum or a minimum?
a. maximum
b. minimum
c. neither
d. both
3. a ball is thrown into the air with an initial upward velocity of 46ft/s. its height (h) in feet after t seconds is given by the function h=-16t^2+46t+6. after how many seconds will the ball hit the ground?
a. 3
b. 4
c. 5
d.6
4. a ball is thrown into the air with an initial upward velocity of 60ft/s. its height (h) in feet after t seconds is given by the function h=-16t^2+6. what will the height be at t=3 seconds
a. 35 feet
b. 40 feet
c. 42 feet
d. 45 feet
5. solve. x^2-121=0
a.0
b. -11
c.11
d.11,-11
6. solve by factoring m^2+8m+7=0
a.8,7
b. -7,1
c. -7,-1
d.7,1
7. solve by factoring n^2+2n-24=0
a.-12
b.-2,12
c.-6,4
d. -4,6
8. one more rectangular-shaped piece of metal siding needs to be cut to cover the exterior of a pole barn. the area of the piece of 30 ft^2. the length is 1 less than 3 times the width. how wide should the metal piece be? round to the nearest hundredth of a foot.
a. 3.33ft
b. 4.3 ft
c. 1 ft
d. 30 ft

The questions are illustrations of quadratic functions

(1) The vertex of the graph

This is the minimum or the maximum point on the graph;

From the attached graph, the maximum point is (1,3).

Hence, the vertex is (b) (1,3)

(2) The vertex type

As mentioned in 1 (above), the vertex is a maximum

(3) Ball thrown upward

The height function is given as:

When the ball hits the ground, the value of h is 0 (this is so, because the height of the ball is 0).

So, we have:

Using a graphing calculator, we have:

t = 3 or t = -0.125

Time cannot be negative.

Hence, the ball hits the ground after (a) 3 seconds

(4) Ball thrown upward

The height function is given as:

At t = 3 seconds, we have:

The height cannot be negative;

Hence, none of the options is correct

(5) Solve

Add 121 to both sides

Take square roots of both sides

Hence, the solution is (d) 11, -11

(6) Solve

Expand

Factorize

Factor out m + 7

Solve for m

or

Hence, the solution is (c) -7, -1

(7) Solve

Expand

Factorize

Factor out n + 6

Solve for n

or

Hence, the solution is (c) -6, 4

(8) Rectangle

Represent the length with l, and the width with w.

So, we have:

The area of a rectangle is

Substitute 3w - 1 for l

Expand

Substitute 30 for area (A)

Rewrite as:

Expand

Factorize

Factor out w + 3

Solve for w

or

The width cannot be negative.

Hence, the metal piece should be (a) 3.33 ft wide

Read more about quadratic functions at:

link

x=half

step-by-step explanation: